Step-by-step explanation:
By rearranging the ages in increasing order;
22,28,32,40,40,50,55,57
Median = (40+40)÷2
= 80 ÷ 2
= 40
Mode = 40
( The value that occurs most)
Range = Highest value - Lowest value
= 57 - 22
= 35
Alberto gets a fish tank
Jackson is on point. Of all fish, catfish make up one-third of the total.
How much gravel does Alberto add to the tank in pounds?The United States of America, Great Britain, and other English-speaking countries predominately utilise the pound as a unit of weight.
Any quantity associated with something is assumed to contain one pound if it does. The pound is the most widely used weight unit in the English-speaking world, including Britain, America, and other nations.
Zebra danios make up half of all the fish.
More fancy guppies than catfish, by a factor of two.
x = guppies
2x = catfish
x + 2x = 1/2 of the fish population
3x = 1/2 of the fish population
3x * 2 = 6x
x = 1/6 number of fancy guppies
catfish:
2x = 2(1/6) = 2/6 = 1/3 catfish.
Jackson is on point. Of all fish, catfish make up one-third of the total.
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The complete question is,
Alberto puts 3 kinds of fish in his fish tank: zebra danios, fancy guppies, and cat fish. Half of Alberto's fish are zebra danios. He has 2 times as many catfish as he has fancy guppies. Alberto's friend Jackson says 1/3 of Alberto's fish are catfish. Is Jackson correct?
A principal of $1500 is invested at 8.5% interest, compounded annually.
How much will the investment be worth after 14 years?
Use the calculator provided and round your answer to the nearest dollar.
The investment will be worth approximately $4468 after 14 years.
What is annual interest rate?Annual interest rate is the rate at which an investment or loan grows in value over the course of a year, expressed as a percentage. It represents the cost of borrowing or the return on investment over one year.
According to question:The following equation can be used to determine the future value of an investment using compound interest:
FV = P * (r/n + 1)(n*t)
Where:
FV is the investment's future value.
The principal is P. (initial investment)
The annual interest rate is represented by r,
The number of times the interest is compounded annually by n (expressed as a decimal).
t is the time (in years)
In this case:
P = $1500
r = 8.5% = 0.085
n = 1 (compounded annually)
t = 14
With these values entered into the formula, we obtain:
FV = 1500 * [tex](1 + 0.085/1)^(1*14)[/tex]
= $4467.56
Therefore, the investment will be worth approximately $4468 after 14 years.
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Use the following number line to choose the correct statement. R x P > S S > Q × R Q × R > S
Answer:
Looking at the number line, we can see that R is to the left of P, and S is to the right of P. Also, Q is to the left of R, and S is to the right of Q.
So, the first statement "R x P > S" is not true, because S is to the right of both R and P.
The second statement "S > Q x R" is also not true, because Q is to the left of R, and S is to the right of both Q and R.
The third statement "Q x R > S" is true, because Q is to the left of R, and S is to the right of both Q and R. Therefore, the correct statement is:
Q x R > S
An economy is operating with output $400 billion above its natural level, and fiscal policymakers want to close this expansionary gap. The central bank agrees to adjust the money supply to hold the interest rate constant, so there is no crowding out. The marginal propensity to consume is 3/4, and the price level is completely fixed in the short run.
to close the expansionary gap, the government would need to increase or decrease spending by $ billion.
Hence, to close the expansionary gap, the government would need to decrease spending by $100 billion.
To close the expansionary gap, the government would need to decrease spending by $100 billion.
The formula to calculate the change in equilibrium output due to a change in government spending is:
∆Y = (∆G / (1 - MPC))
Where:
∆Y = change in equilibrium output
∆G = change in government spending
MPC = marginal propensity to consume
Here, the output is $400 billion above its natural level, and the central bank agrees to adjust the money supply to hold the interest rate constant, so there is no crowding out. Therefore, we can assume that the change in government spending (∆G) would have a one-to-one effect on the equilibrium output (∆Y).
Given that MPC = 3/4, we can plug in the values into the formula:
400 = (∆G / (1 - 3/4))
∆G = (1 - 3/4) * 400
∆G = (1/4) * 400
∆G = 100
Hence, to close the expansionary gap, the government would need to decrease spending by $100 billion.
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Choose scales for the coordinate plane shown so that you can graph the points J (5, 50), K(3, 50), L (4, -40), M (-2, 40), and N (-5, -10). on the x-axis use a scale of ____ units for each grid square. on the y-axis use a scale of ____ units of each grid square. complete the explanation for using these scales for each axis. the x-coordinates range from ____ to ____, and the y-coordinates range from ____ to ____.
On the x-axis use a scale of 2 units for each grid square. on the y-axis use a scale of 10 units of each grid square. The x-coordinates range from -5 to 5. y-coordinates range from -40 to 50.
What is coordinate plane?In mathematics, points and functions are represented and graphed on the coordinate plane, commonly known as the Cartesian plane. The x-axis and y-axis are two perpendicular number lines that meet at the origin to form the plane (0,0).
On the coordinate plane, points are denoted by ordered pairs (x, y), where x denotes the point's separation from the y-axis and y denotes its separation from the x-axis.
For the given coordinates the range of x and y coordinates are:
x-coordinates range from -5 to 5
y-coordinates range from -40 to 50.
Thus, we use a scale of 2 on the x-axis and 10 units on the y axis.
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The sum of a number and three is no more than eight
Answer:5
Step-by-step explanation: hope this helps
Suppose that the function h is defined as follows.
if
-2
-1
h(x)= 0
1
2
Graph the function h.
-3.5
if-2.5
if-1.5
if -0.5
if 0.5 ≤x≤1.5
Suppose that the function h is defined as follows. -2 -1 h(x)= if – 2, the graph is given below: (see image)
What is a Graph?A graph is a mathematical structure used to represent relationships between objects or entities. It consists of a set of vertices (also known as nodes) and a set of edges that connect pairs of vertices.
In a graph, the vertices represent the objects or entities being studied, while the edges represent the connections or relationships between them.
For example, in a social network graph, the vertices might represent individual users, and the edges might represent their connections (e.g. friendships) with other users.
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Which of the numbers 0, 1, 2, 3 or 4 make the equation 8/y2 + 2 true?
None of the given numbers make the equation 8/y² + 2 true.
What is algebra?
Algebra is a branch of mathematics that deals with mathematical operations and symbols used to represent numbers and quantities in equations and formulas.
To solve this problem, we can substitute each of the given numbers (0, 1, 2, 3, 4) for y in the equation 8/y² + 2 and see if the equation is true.
Substituting y=0 would make the denominator of the fraction zero, which is undefined, so y=0 is not a valid choice.
Substituting y=1 would give us:
8/1² + 2 = 8 + 2 = 10
So, 1 is not the answer.
Substituting y=2 would give us:
8/2² + 2 = 8/4 + 2 = 2 + 2 = 4
So, 2 is not the answer.
Substituting y=3 would give us:
8/3² + 2 = 8/9 + 2 = 0.888 + 2 = 2.888
So, 3 is not the answer.
Substituting y=4 would give us:
8/4² + 2 = 8/16 + 2 = 0.5 + 2 = 2.5
So, 4 is not the answer.
Therefore, none of the given numbers make the equation 8/y² + 2 true.
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Elliot read a report from a previous year saying that 6 % 6%6, percent of adults in his city biked to work. He wanted to test whether this had changed, so he took a random sample of 240 240240 adults in his city to test H 0 : p = 0.06 H 0 :p=0.06H, start subscript, 0, end subscript, colon, p, equals, 0, point, 06 versus H a : p ≠ 0.06 H a :p =0.06H, start subscript, start text, a, end text, end subscript, colon, p, does not equal, 0, point, 06, where p pp is the proportion of adults in Elliot's city that bike to work. The sample results showed 21 2121 adults who biked to work, and the corresponding test statistic was z ≈ 1.79 z≈1.79z, approximately equals, 1, point, 79. Assuming that the necessary conditions are met, what is the approximate P-value for Elliot's significance test?
Answer: To find the P-value, we first need to determine the direction of the alternative hypothesis. Since the alternative hypothesis is two-tailed, we need to divide the significance level (α) by 2 before finding the critical values and the rejection region. Therefore, we have:
H0: p = 0.06
Ha: p ≠ 0.06
α = 0.05/2 = 0.025
The test statistic is z = 1.79, which represents the number of standard errors that the sample proportion is from the hypothesized population proportion under the null hypothesis. We can find the P-value by looking up the area in the standard normal distribution table beyond the test statistic in both tails:
P-value = P(Z ≤ -1.79 or Z ≥ 1.79)
= P(Z ≤ -1.79) + P(Z ≥ 1.79)
= 0.0364 + 0.0364
= 0.0728
Therefore, the approximate P-value for Elliot's significance test is 0.0728. Since the P-value is greater than the significance level of 0.05, we fail to reject the null hypothesis and conclude that there is not enough evidence to suggest that the proportion of adults who bike to work in Elliot's city has changed significantly from the previous year.
Step-by-step explanation:
A car, van, truck and bike are all travelling in the same direction on the road. Each travels at a constant speed, but the speeds of the 4 vehicles may be different. At 10 am the car overtakes the van. At noon it overtakes the truck. At 2 pm it overtakes the bike. At 4 pm the truck overtakes the bike. At 6 pm the van overtakes the truck. When does the van overtake the bike?
Answer:
at 6 pm
Step-by-step explanation:
I'm 99.9% sure that it's correct, please tell me if I'm wrong
Luisa has great news, she communicates it to 3 people. Each of them tells 3 more. This is how a chain is set up, since each new person who learns the news communicates it to three others. It takes one person approximately 10 minutes to communicate the news to three others. If an hour has passed, how many people have heard the news?
Answer:
The amount of persons who have heard in 30mins would be:
45 persons
Jeremy and Aksa were finding the volume of this prism. They agreed that 4 layers can be added together to find the volume. Jeremy says that he can see on the end of the prism that each layer will have 16 cubes in it. Aksa says that each layer has 24 cubes in it. Who is right? Explain your answer.
Both Jeremy and Aksa could be right, depending on how they are counting the cubes for finding the volume of a prism.
What is a prism?A prism is a three-dimensional solid shape with a constant cross-section, usually a polygon. It is characterized by two identical end faces, parallel and congruent bases, and straight lateral faces connecting the bases.
According to the given information:Both Jeremy and Aksa could be right, depending on how they are counting the cubes.
If the prism has a square base with 4 cubes along each side, then there would be 16 cubes in each layer. If there are 4 layers, then the total volume would be 16 x 4 = 64 cubic units.
However, if the prism has a rectangular base with 6 cubes along one side and 4 cubes along the other side, then there would be 24 cubes in each layer. If there are 4 layers, then the total volume would be 24 x 4 = 96 cubic units.
Therefore, the answer depends on the shape of the prism and how the layers are counted.
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Evaluate the expression for the given value.
–a – 7 for a = –4
A11
B–11
C3
D–3
On a given planet, the weight of an object varies directly with the mass of the object. Suppose that an object whose mass is 2 kg weighs 4 N. Calculate the mass of another object that weights 18 N.
Answer:
Let m be the mass of the object and w be the weight of the object. According to the problem, weight varies directly with mass, so we can write:
w = k * m
where k is the constant of proportionality.
To find k, we can use the information given in the problem. We know that when m = 2 kg, w = 4 N. Substituting these values into the equation above, we get:
4 N = k * 2 kg
Solving for k, we get:
k = 4 N / 2 kg = 2 N/kg
Now we can use this value of k to find the mass of an object that weighs 18 N. We can rearrange the equation above to solve for m:
m = w / k
Substituting w = 18 N and k = 2 N/kg, we get:
m = 18 N / 2 N/kg = 9 kg
Therefore, the mass of the object that weighs 18 N is 9 kg.
Find the area of a rectangle with length 4.3 cm and breadth 3.9 cm
Answer:
16.77 cm²
Step-by-step explanation:
Area of rectangle = L x W
L = 4.3 cm
Width = 3.9 cm
Let' solve
4.3 x 3.9 = 16.77 cm²
So, the area of the rectangle is 16.77 cm²
name three solution for h > 8
Answer:
all numbers greater than 8
Step-by-step explanation:
simply pick any number greater than 8, since the > symbol is in front of 8. By the way, you cannot pick 8. :) I hope this helps!
if you dilate triangle ABC by a scale factor of 3 and (0,0) is the center, what will be the length of AB?
the new length of AB after a dilation by a scale factor of 3 with (0,0) as the center would be 3 times the original length of AB.
How to solve the question?
To find the new length of AB after a dilation by a scale factor of 3 with (0,0) as the center, we can use the following formula:
AB' = AB x 3
where AB' is the length of AB after the dilation, and AB is the original length of AB.
However, we need to first determine the length of AB in the original right triangle ABC. To do this, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
Let's assume that AB is the hypotenuse of the right triangle ABC, and that AC and BC are the other two sides. Then we have:
AB²= AC²+ BC²
Without more information about the lengths of AC and BC, we cannot determine the value of AB. However, once we have determined the length of AB, we can use the formula above to find the new length of AB after dilation.
Assuming we know the length of AB in the original right triangle ABC, we can now use the formula for dilation to find the new length of AB:
AB' = AB x 3
For example, if AB is 5 units long in the original triangle, then after dilation, AB' would be:
AB' = 5 x 3 = 15 units
Therefore, the new length of AB after a dilation by a scale factor of 3 with (0,0) as the center would be 3 times the original length of AB.
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Need help with is question
Answer:
27.78%
Step-by-step explanation:
To calculate the percentage of the total spending that is on rent, we need to divide the amount spent on rent by the total amount spent, and then multiply by 100 to get the percentage.
Total spending = food + rent + other + fun
Total spending = $400 + $500 + $600 + $300
Total spending = $1800
So, the percentage of the total spending that is on rent is:
($500 / $1800) x 100% = 27.78%
Therefore, approximately 27.78% of the total spending is on rent.
The table contains some points on the graph
of an exponential function. Based on the
table, which function represents the same
relationship?
Answer: 1st one
Step-by-step explanation:
What is the range of the relation whose graph is shown?
The range of the relation whose graph is shown include the following: C. -1 ≤ y ≤ 1.
What is a domain?In Mathematics and Geometry, a domain is the set of all real numbers for which a particular function is defined.
Additionally, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.
By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:
Domain = {-4, 4} or -4 ≤ x ≤ 4.
Range = {-1, 1} or -1 ≤ y ≤ 1.
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7. Can the following be the lengths of the sides of a triangle?
a. 20 cm, 40 cm, 50 cm
b. 20 cm, 40 cm, 60 cm
c. 41 cm, 250 mm, 12 cm
Answer:
B
Step-by-step explanation:
THE TWO SMALLER SIDES = THE LARGER SIDE HENCE ITS A TRIANGLE
A waiter made $288 in tips after waiting on 12 tables. What was the waiter’s average tip per table?
A$24
B$13
C$15
D$16
Answer:
24
Step-by-step explanation:
Answer:
A. $24
Step-by-step explanation:
Given:
total of $288number of values is 12 tablesSolve for average tip:
Average is the same as the meanTo solve you have add up the total and divide by the total number of values288 / 12 = 24Answer:
Thus, the waiter's average tip per table is $24.
The answer is A.
Use the slip and y-intercept to identify the equation of this line
Answer:
y=2x
Step-by-step explanation:
equation formula is y=mx+b
m is slope
b is y-intercept
you know that slope is 2
y intercept is 0
so plug it into the equation
y=2x+0 or just y=2x
A machine in a factory makes chairs at rate of two chairs every 10 minutes how much time does the machine take to make five chairs how many minutes would it take for the factory to fulfill an order for 32 chairs show your work or explain how you determine your answers
The width of the set of the shelves needs to be 5 times the height of the set of shelves and the set of shelves must have three shelves If there are 80 feet of wood to use to build the set of shelves what should the dimensions the set of shelves be?
The dimensions of the set of shelves should be approximately 4.21 feet in height and 21.05 feet in width.
What is a linear equation?When plotted on a coordinate plane, an algebraic equation known as a linear equation looks like a straight line. The variable (or variables) in this equation always have a greatest power of 1, making it a constant. In other words, a linear equation simply makes use of the fundamental operations of addition, subtraction, and multiplication of variables to the first power, as well as constants.
Given:
Width of the set of shelves = 5 times the height of the set of shelves
Number of shelves = 3
Total amount of wood available = 80 feet
Let's denote the height of the set of shelves as "h" and the width of the set of shelves as "w".
Using the first given information, we can write the equation:
Width (w) = 5 times the height (h) ==> w = 5h
Next, we know that the set of shelves has 3 shelves, so the number of shelves is fixed at 3.
Finally, we are given that we have 80 feet of wood available to build the shelves.
Using these equations, we can substitute w = 5h into the equation for the total amount of wood:
3w + 4h = 80
Substituting w = 5h, we get:
3(5h) + 4h = 80
15h + 4h = 80
19h = 80
h = 80/19
So, the height of the set of shelves is approximately 4.21 feet.
Now, substituting this value of h back into w = 5h, we get:
w = 5(4.21)
w = 21.05
So, the width of the set of shelves is approximately 21.05 feet.
Therefore, the dimensions of the set of shelves should be approximately 4.21 feet in height and 21.05 feet in width.
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Help pleasee
The half-life of Palladium-100 is 4 days. After 16 days a sample of Palladium-100 has been reduced to a mass of 2 mg.
What was the initial mass (in mg) of the sample? --------------
What is the mass 7 weeks after the start?-------------
The initial mass (in mg) of the sample is 32 mg
The mass 7 weeks after the start is 0.198 mg
What is exponential decay:Exponential decay is a process in which a quantity decreases at a rate proportional to its value. This means that the larger the quantity, the faster it will decrease.
Exponential decay is modeled by the following formula:
[tex]A = A_{0} \times (1/2)^{\frac{t}{T} }[/tex]
where A is the amount after time t, A₀ is the initial amount,
T is the half-life, and t is the time elapsed
Here we have
The half-life of Palladium-100 is 4 days. After 16 days a sample of Palladium-100 has been reduced to a mass of 2 mg.
For the first question, we know that after 16 days, the amount is 2 mg, and the half-life is 4 days. We can plug these values into the formula:
[tex]2 = A_{0} \times (1/2)^{\frac{16}{4}}[/tex]
Simplifying, we get:
2 = A₀ × (1/2)⁴
2 = A₀ × (1/16)
A₀ = 2 × 16
A₀ = 32 mg
So the initial mass of the sample was 32 mg.
For the second question, we need to find the mass after 7 weeks, or 49 days. We can use the same formula, but with t = 49:
[tex]A = 32 \times (1/2)^{\frac{49}{4} }[/tex]
A ≈ 0.198 mg
Therefore,
The initial mass (in mg) of the sample is 32 mg
The mass 7 weeks after the start is 0.198 mg
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The owner of a sports complex wants to carpet a hallway connecting to buildings. The carpet costs $1.50 per square foot. How much does it cost to carpet the hallway?
Answer:
$526.75 i believe
Step-by-step explanation:
a right triangle has a hypotenuse of length 7 inches. If one angle is 38 degrees, find the length of each leg.
Check the picture below.
[tex]\sin(38^o )=\cfrac{\stackrel{opposite}{x}}{\underset{hypotenuse}{7}}\implies 7\sin(38^o)=x\implies 4.31\approx x \\\\[-0.35em] ~\dotfill\\\\ \cos(38^o )=\cfrac{\stackrel{adjacent}{y}}{\underset{hypotenuse}{7}}\implies 7\cos(38^o)=y\implies 5.52\approx y[/tex]
Make sure your calculator is in Degree mode.
Answer:
4.31 in5.52 inStep-by-step explanation:
You want the leg measures in a right triangle with a hypotenuse of 7 inches and an angle of 38°.
Trig functionsThe mnemonic SOH CAH TOA reminds you of the relations between side lengths and trig functions:
Sin = Opposite/Hypotenuse ⇒ Opposite = Hypotenuse×Sin
Cos = Adjacent/Hypotenuse ⇒ Adjacent = Hypotenuse×Cos
ApplicationThe given triangle will have opposite and adjacent sides of ...
opposite = (7 in)sin(38°) ≈ 4.31 in
adjacent = (7 in)cos(38°) = 5.52 in
The leg lengths of the triangle are 4.31 inches and 5.52 inches.
The sum of 2 vector forces is <5, -3>. What is the magnitude of the resulting force?
According to the question the magnitude of the resulting force is 5.83.
What is magnitude?Magnitude is a measure of the size or intensity of a physical quantity. It is an expression of how large or small a quantity is in comparison to a reference value. Magnitude is typically used in physics and astronomy, but it can also be used in other areas such as engineering and seismology. Magnitude is not an absolute measurement; rather, it is a relative measure of how much larger or smaller one quantity is compared to another. For example, the magnitude of a star's brightness is a measure of how much brighter it is compared to other stars.
The magnitude of the resulting force can be calculated using the Pythagorean theorem. The formula for calculating the magnitude of a vector is:
[tex]\sqrt[]{(x2 + y2)}[/tex]
In this case, x = 5 and y = -3, which gives us:
[tex]\sqrt{(52 + (-3)2)}[/tex] = [tex]\sqrt{(25 + 9)}[/tex] = √[tex]\sqrt{(34)}[/tex] = 5.83.
Therefore, the magnitude of the resulting force is 5.83.
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How do I solve this problem?
The measure of angle CFE is determined as 29⁰.
What is the measure of angle CFE?The measure of angle CFE is calculated by applying the following formula.
The intersecting chord theorem, also known as the intersecting chords inside and outside theorem, is a geometric property that applies to chords (line segments that connect two points on the circumference of a circle) that intersect inside or outside a circle.
Based on the angle of intersecting chord theorem, we will have the following equation.
m∠CFE = ¹/₂( arc angle CE )
arc CE = 360 - 302 (sum of angles in a circle)
arc CE = 58⁰
m∠CFE = ¹/₂ x 58
m∠CFE = 29⁰
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